There have been angry clashes between Russian and US envoys at the UN Security Council, after the US called a meeting to discuss Moscow's troop build-up on its borders with Ukraine.
US Ambassador Linda Thomas-Greenfield said the mobilisation was the biggest Europe had seen in decades.
Her Russian counterpart accused the US of fomenting hysteria and unacceptable interference in Russia's affairs.
The US and UK have promised further sanctions if Russia invades Ukraine.
UK Foreign Secretary Liz Truss said legislation was being prepared which would target a wider range of individuals and businesses close to the Kremlin than is currently possible.
A US official said Washington's sanctions meant individuals close to the Kremlin would be cut off from the international financial system.
Russia has placed an estimated 100,000 troops, tanks, artillery and missiles near Ukraine's frontiers.
Meanwhile, diplomatic efforts continue, with US Secretary of State Antony Blinken due to hold talks with Russian Foreign Minister Sergei Lavrov later on Tuesday.
The US says it has now received a written response from Russia to a US proposal aimed at de-escalating the crisis in Ukraine.
A state department spokesperson said it would be "unproductive" to negotiate the response in public. The spokesperson added that the US remained fully committed to dialogue and would continue to consult closely with its allies and partners, including Ukraine.
Also on Tuesday, UK Prime Minister Boris Johnson is travelling to Ukraine's capital Kyiv. He has promised to work with Ukrainian President Volodymyr Zelensky to find a diplomatic solution to arguments with Moscow and "avoid further bloodshed".
